Sustaining Fiscal Policy Through Immigration1
Kjetil Storesletten
Institute for International Economic Studies
Stockholm University
October 1, 1999
First submission, February 27, 1997
Forthcoming in the Journal of Political Economy. I owe special thanks to Jose Vctor Ros-Rull and
Finn E. Kydland for their valuable guidance and suggestions. I am also grateful for comments and help from
Michele Boldrin, Christina Lonnblad, Dennis Epple, John Hassler, Alan Head, Stephane Pallage, Torsten
Persson, Seth Sanders, and two anonymous referees. All errors are my own.
1
Abstract
Using a calibrated general equilibrium overlapping generations model, which explicitly accounts for dierences between immigrants and natives, this paper investigates if an immigration policy reform alone could resolve the scal problems associated with the ageing of the
baby boom generation. Such policies are found to exist and are characterized by increased
inow of working-age high- and medium-skilled immigrants. One particular feasible policy
involves admitting 1.6 million 40{44 year old high-skilled immigrants annually. These ndings are illustrated by computing the discounted government gain of admitting additional
immigrants, conditional on their age and skills.
1 Introduction
The scal implications of immigration to the US are, potentially, very large, not only because
the inow of immigrants is strong - about 1.1 million per year - but also since immigrants are
younger than Americans and have a wider distribution of skills. If skilled workers immigrate
and immediately start paying taxes, the net scal eects are likely to be large and positive,
even when the gains are traded o with the subsequent costs of retirement. Moreover, young
immigrants would alleviate the current demographic imbalance, but without a twenty-year
period of childhood. Thus, selective immigration should be able to mitigate some of the scal
burden associated with the ageing of the baby boom generation and might, to some extent,
serve as an alternative to tax hikes or spending cuts for nancing future scal decits.1
This paper explores if a selective immigration policy alone could be used as an instrument
to balance the budget and avoid scal reform altogether. The ndings are illustrated by
computing the net government gain, in present value terms, of admitting one additional
immigrant, conditional on skills and age at the time of immigration.
The framework is a dynamic equilibrium model of population transition, closely related to
Auerbach and Kotliko (1987). Immigration is given by a selective immigration policy determining the age and skill structure and the annual inow of new immigrants. Natives and
immigrants in the model economy dier in age, skills, and fertility. In addition, immigrants
are dierentiated by age at the time of immigration and by their legal status. The overlapping generations framework captures the rst-order eects of immigration: an inow of
working-age immigrants increases tax revenues per capita and reduces government debt and
government expenditures per capita. When immigrants retire, these eects are reversed. A
general equilibrium analysis is required since the government budget is also aected through
increases in interest rates and decreases in wages, due to a rise in the labor-capital ratio (assuming capital does not ow into the country in response to immigration). Higher interest
rates increase the cost of servicing the public debt, and lower wages reduces tax revenues.
I nd that selective immigration policies, involving increased inow of working-age highand medium-skilled immigrants, can remove the need for a future scal reform. In contrast, increased inow of immigrants with the age- and skills-composition of average current
immigrants cannot, in itself, induce long-run budget balance. As a benchmark, I compute
the smallest increase in annual immigration required to balance the budget, given that the
government is free to choose the distribution of age and skills of new immigrants, while restricted to keeping the current tax and spending policies unchanged. This minimum change
involves increasing annual immigration from 0.44% to 0.62% of the population, or about 1.6
million, provided all new immigrants are high-skilled and 40{44 years old. Admitting adult
immigrants but excluding their children may not be politically feasible, however. If immigrants were instead admitted in family units, the minimum number of immigrants required
1
would increase to 1.08% of the population annually - assuming the head of the family to be
high-skilled and 45{49 years old. While admitting 1.6 million immigrants annually might
seem like a considerable policy change, it is illuminating to contrast this to an alternative
scal reform: income taxes would have to increase by 4.4% points if one opted for changing
taxes instead of immigration policy or government expenditures. Thus, it seems sensible
to consider at least marginal immigration policy reforms as part of a larger scal reform
package.
These ndings are driven by the following results: Under the current scal policy and the
immigration policy outlined above, the discounted value of future tax receipts less government expenditures associated with an additional immigrant varies considerably with age and
skills and reaches a maximum of $177,000, or seven times GNP per capita, for high-skilled
immigrants arriving when they are 40{44 years old. This includes the cost of future descendants. The average NPV of representative high-, medium-, and low-skilled legal immigrants
are found to be $96,000, -$2,000, and -$36,000, respectively. In comparison, the NPV of a
newborn native is -$88,000.
All age proles of NPV for new immigrants are hump-shaped and peak between the age of
35 and 44. The timing of the peak is robust to several changes in the model setup, due to
a basic trade-o between a longer remaining working life on the one hand, and a smaller
number of new children on the other. Abstracting from the cost of future children would
increase the average discounted gain by $20,000 and make the age proles peak earlier. If,
alternatively, family migration is considered (immigrants bringing existing children when
immigrating), the maximum NPV falls to $140,000 per 40-44 year old high-skilled head of
household.
To the extent that one is willing to consider using the immigration policy for enriching public
coers, the paper oers several immediate policy implications. The analysis suggests which
groups of immigrants to target, if the aim is to maximize the public coer contribution per
immigrant. For instance, the Canadian \point system" for allocating visas to prospective
immigrants favors skilled immigrants in the age group 20{40. My calculations suggest,
however, that focusing on high-skilled immigrants in the age group 20{49 would make more
sense if the objective is to maximize the public gain, as the NPV of high-skilled immigrants
between 40 and 49 far exceeds that of 20{24 year old high-skilled immigrants.
Moreover, the results indicate that the discounted government cost of new illegal immigrants
can be as large as $54,000 per immigrant, compared with $36,000 for legal low-skilled immigrants. If curbing illegal immigration is infeasible, these results suggest that converting
young illegal immigrants to legal ones, along the lines of the Immigration Reform and Control Act of 1986, is benecial, provided the ow of illegal immigrants is not aected by this
amnesty policy.
2
Finally, I nd that return migration decreases the discounted contribution of high-skilled
immigrants under 50. Thus, policies which lower the return migration probability for this
group might improve public nances. Straightforward examples of such reforms would be to
make the rules for allocating visas and green cards to immigrants already working in the US
less strict, and to automatically grant green cards to foreign students upon graduation.
Despite the strong implications of immigration for public nance, surprisingly few studies
address the cost-benet aspect of immigration.2 Borjas (1994), Huddle (1993) and Passel
(1994) compute the net government surplus in a particular year, stemming from the crosssection of immigrants currently residing in the US. The key shortcomings of this approach
are that the instantaneous scal impact of immigrants changes with their age structure, and
that costs and expenditures occurring later in the life of an immigrant (e.g. pensions) should
be discounted. Simon (1984) and Akbari (1989) compute the tax revenues and government
expenditures directly associated with dierent immigration cohorts. These are used as a
stand-in for a time prole of net contributions which, in turn, are discounted to get a crude
measure of the \net public gain". These studies ignore the descendants of immigrants, the
changes in the age- and skill-proles of immigrants, and the general equilibrium interaction between immigrants and an ageing population. Canova and Ravn (1998) study the
macroeconomic eects of low-skilled immigration in an innitely lived agent model, ignoring
life-cycle aspects altogether. Auerbach and Oreopoulos (1999) and Bonin, Raelhuschen and
Walliser (1997) include dynamic eects of immigration through partial equilibrium generational accounting exercises for the US and Germany, respectively. Lastly, Storesletten (1995,
1996) and Lee and Miller (1997) (on which Chapter 7 in Smith and Edmonton (1997) is
based upon) compute the net present value of the scal impact of new immigrants, including
their decendants.
The paper then proceeds as follows. The model economy and the competitive equilibrium
are dened in Section 2. The parameterization of the economy is described in Section 3, and
the results are reported in Section 4. Section 5 concludes.
2 The model
2.1 Population process and heterogeneity
The economy is populated by agents who live a maximum of I periods. Agents dier in
age, skills, legal status (native, legal immigrant, or illegal immigrant), and, if an immigrant,
the age at the time of immigration. The \type" of an agent is denoted by (i; s), where i is
age, s(1) is the age at the time of immigration (natives have s(1) = 1), s(2) is skill, and
s(3) is legal status. The key dierence between natives and legal immigrants in the model
3
is in terms of labor productivity and fertility. Distinguishing immigrants by legal status is
important because illegal immigrants might be very dierent from legal ones, with respect to
their impact on public coers. Moreover, illegal immigration constitutes a substantial share
of the migration to the US (Chiswick (1988)).
The immigrants' skills (or education) take on three values; low-skilled, medium-skilled and
high-skilled. Skills are exogenous and do not change during an agent's lifetime. For simplicity, the skills of natives are assumed to be homogeneous (conditional on age).
Children of immigrants, born after their parents immigrated, are considered as natives.
Thus, the skills of second-generation immigrants are assumed to be independent of the skills
of their parents. Following Lee (1974) and Ros-Rull (1992), the number of newborn natives
in period t is given by
X
# newbornt = i;si;s;t + yt;
(1)
i;s
where i;s;t is the number of type (i; s) agents in period t, i;s are type-specic fertility rates
averaged over time, and yt is a deterministic process. Agents do face longevity uncertainty,
however, and the probability of surviving to age i + 1, conditional on being alive at age i, is
given by i .
A selective immigration policy is chosen by the government and determines annual immigration and the distribution of age and skills of new legal immigrants, as a function of
the state of the economy. I assume that the government cannot alter the ow of illegal immigrants. There are numerous ways of specifying the possible immigration policies. I focus
on a very simple type of policies where the inow of each age and skill group is some xed
fraction of the size of the population.
Empirical studies have documented that as many as 18-20% of the new immigrants return
to their respective home countries within ten years after their rst arrival to the US (Borjas
and Bratsberg (1996), Jasso and Rosenzweig (1982) and Warren and Peck (1980)). The
probability of return migration, j , is assumed to simply depend on the length of the spell
in the host country (where j stands for years since immigration). Moreover, to ensure
that immigrants do not take the event of return migration into consideration when making
decisions, I assume that the agents who return migrate will face the same prices, transfers,
and taxes in their home country as they would have faced in the US.
2.2 Preferences, technology, and government
Agents derive utility from leisure 1 ; n and a standard consumption good c. Those below
age are dened as children. They consume the transfers they get from the government
and do not work. Furthermore, agents do not care about their children and have no bequest
4
motives, although they may end up leaving accidental bequests. At age , all agents retire.
A type s agent maximizes her expected lifetime utility, given by
max E
fc ;n g
i
i
I
X
i=maxfs(1); g
iu(ci; ni ) = fmax
c ;n g
i
i
I
X
i=maxfs(1); g
1; 1;
i (ci (1 ;1 n;i) )
iY
;1
j =s(1)
j ;
(2)
subject to the intertemporal budget constraint and the pension system.
Output in period t is given by a standard constant return to scale production function
zt f (Kt; Nt ) with aggregate labor Nt and capital Kt as inputs. The exogenous productivity
level, zt , is growing at a deterministic rate. Output is used for consumption and investment
in new capital. Labor productivity of an agent is measured in equally productive eciency
units, which implies that native and immigrant labor are perfect substitutes, and that Nt
is given by the sum of eciency units supplied by agents. Firms rent labor and capital on
spot markets at a given wage rate Wt and a net rental rate Rt and solve a standard prot
maximzation problem, maxK;N fzt f (K; N ) ; (Rt + )K ; Wt N g, where is the depreciation
rate for capital.
Fiscal policy is given exogenously and consists of a tax rule, a public spending rule, and a
transfer rule. The tax rule species a constant payroll tax rate p, and a constant tax rate
on capital and labor income. Natives and legal immigrants are taxed at the same rates.
Illegal immigrants dier from their legal counterparts in that they pay no taxes and receive
no government transfers. They are assumed, however, to incur public consumption at the
same rate as their legal counterparts.
Public consumption is given by a rule determining government purchases of goods and services as a function of population and time:
Gt (1 + ;)t
X
i;s
gi i;s;t;
(3)
where gi is government consumption per agent of age i in period zero and ; is the rate of
growth in GNP per capita in steady state. Conditioning the incidence of public consumption
on age is important, since large components of government purchases of goods and services
are age dependent (e.g. the schooling system).
The Social Security system is modeled explicitly. Old Age Insurance benets (OAI) are paid
to retired agents only and are a function h(:) of the individual's average indexed monthly
earnings (AIME) during her time in the work force. The remaining components of Social
Security, plus all other government transfer programs, are modeled as age-specic lump sum
transfers i.3 All benets are assumed to be tax exempted. The results are very robust to
this assumption (Storesletten (1999)).
Residence in the US when retired is not a requirement for collecting benets. Let ^i;s;t denote
5
the number of living return migrated legal immigrants of type s who qualify for full Social
Security benets, let ^i be their lump sum transfers, and assume that only a fraction of
these actually collect their benets. The aggregate government transfers in period t can then
be computed as
Tt +
8
X< X
i;s;t(1 + ;)t i
:
s2L i=s(1)
I X
i= +1
+
i;s;t (1 + ;)ti + h(di;s;t) +
9
=
^i;s;t((1 + ;)t^i + h(di;s;t)) ; ;
(4)
where di;s;t is the AIME of an agent (i; s) in period t and the condition s 2 L ensures that
illegal immigrants are excluded from Tt . The total tax revenues are given by
Revenuest (1 ; (1 ; p=2)(1 ; ; p=2))WtN^t + Rt A^t;
(5)
where N^t and A^t are aggregate labor input and private nancial wealth of natives and legal
immigrants. Note that the employer part of Social Security contributions is tax deductible.
Budget decits are nanced by increases in government debt, held as bonds Bt by private
agents.
The only individual portfolio constraint is that agents of age I , who will die for sure, cannot
leave negative bequests. There are no annuity markets in the economy, so the agents face the
risk of dying with positive wealth. Each period, accidental bequests are donated to newborn
natives in a lump sum xt . Immigrants are assumed to bring no wealth when they arrive,
while return-migrants bring their savings out of the country when they leave. RMt denotes
the aggregate amount of capital brought out of the economy in period t.
This model specication abstracts from nonrival public goods and congestion eects (scarce
public capital diluted by new immigrants). I will, however, consider the sensitivity of the results to the inclusion of a nonrival public good. One feature of the model which does capture
a public good element of immigration is that the per capita government debt falls as immigration increases. As the model abstracts from government-owned physical capital, parts of
government consumption, gi, can be interpreted as a stand-in for replenishing government
capital per agent of age i. Thus, a potentially increased pressure for public investments due
to immigration is captured in the model, as government consumption is increasing in the
number of new immigrants.
6
2.3 Equilibrium
Given initial conditions for government debt B0 , the error term of the fertility process y0,
and the distributions of assets a0 , past average earnings d0 and population 0 and ^0, an
equilibrium
is dened as a sequence
n
o1
Wt ; Rt ; Nt; Kt; Bt ; RMt ; xt; fni;s;t; ci;s;t; ai;s;t; di;s;t; i;s;t; ^i;s;tgIs;i=s(1) t=0 ,
a tax rate , and an immigration policy rule , such that the following holds
a) The wage rate and rate of return on savings, Wt and Rt , equal net marginal productivities of labor and capital.
b) The aggregate resource constraint holds every period.
c) Each sequence fci;s;t+i; ni;s;t+igIi=s(1) solves the utility maximization problem (2) of
agents of type s who were born in period t ; s(1), subject to their budget constraints,
the pension system, and the price sequence fRt ; Wtg1
t=1 . Moreover, the sequences of
individual wealth and average indexed earnings, fai;s;t+i; di;s;t+igIi=s(1) , are consistent
with the agents' consumption and leisure choices.
d) Aggregate accidental bequests per newborn native in period t, xt , are consistent with
the distribution of assets and population.
e) The government policy ( ; ) is feasible, in the sense that current government debt
equals the net present value of future budget decits and surpluses.
f) The sequence of government debt evolves according to Bt+1 = (1 + Rt )Bt + Tt +
Gt ; Revenuest , and the aggregate gures Nt and RMt are computed by aggregating
individual labor eort and return migrants' wealth holdings.
g) Aggregate capital Kt equals aggregate private wealth minus government debt Bt in
period t.
h) The population sequences ffi;s;t; ^i;s;tgIi=s(1) g1
^0, y0, , and
t=1 are generated by 0 , the mortality, fertility, and return migration processes.
3 Parameterization of the model economy
3.1 Population parameters
The length of a period in the model is taken to be ve years. Each agent retires after period
13 and might live until period 18 (i.e. agents retire at 65 and die before 90). The mortality
7
rates of natives and immigrants are assumed to be identical, xed at the 1988 US levels.
Since many immigrants originate from countries where tropical diseases are common, a case
could be made for immigrants having higher mortality than natives. Shorter longevity would
increase net government benet from immigration so the equal mortality assumption is a
conservative benchmark.
The age-specic average fertility rates in (1) for natives are estimated by averaging over
the 1960{89 time period.4 Storesletten (1995) estimates immigrant women's fertility by
constructing synthetic cohorts from the 1990 and 1980 Census, and computing changes
between 1980 and 1990 in the average number of children for various groups. This approach
implies that the average total fertility rate (TFR) of high-skilled immigrants is 16% lower
than that of natives, while the TFR for medium- and low-skilled immigrants are 7% and
50% higher than that of natives, respectively. The i;s parameters are set accordingly. The
error term yt in (1) follows a deterministic AR(2) process with coecients 1 = 1:28 and
2 = ;0:65, estimated using US data from 1960 to 1990. The 1990 values of the estimated
process are used as the starting point y0.
Return migration appears to be quite high in the rst years after immigration, but declines
sharply over time. As an approximation of the return migration process, I assume that the
return migration rate, j , is constant after the rst period. Warren and Peck (1980) nd that
by April 1970, 18% of the 1960-70 cohort of new immigrants and 5.2% of the immigrants
present in 1960 had emigrated from the US. Using these measurements, I set 1 = 17:06%
and j = 2:63% for all j >= 2.
All alternative immigration policies considered in this paper constitute increased inow,
relative to the status quo immigration policy, of one or several groups of legal immigrants. I
measure the status quo immigration policy, unconditional on legal status, as the distribution
of age and skills of immigrants enumerated in the 1990 Census, who immigrated during the
period 1988-1990. The status quo annual inow of immigrants is 0.44% of the population.
The annual inow of illegal immigrants currently constitutes about 300,000, or 0.12% of the
population, (Fix and Passel (1994)), and I assume this fraction to be constant over time.
All illegal immigrants are assumed to be low-skilled.
Note that the status quo population process implies a lower future dependency ratio (retirees
per worker), after 2010, than the standard alternative projections. For instance, the status
quo case projects a maximum dependency ratio of 0.315 in 2035 (and 0.276 eventually),
compared to 0.369 in 2035 (and 0.421 eventually) for the Social Security Administration
(SSA) projections (Bell (1997)). This discrepancy is due to higher mortality rates, more
immigration, and higher fertility rates (after the year 2000), in the status quo population
process than what is assumed in the SSA projections. Higher fertility rates will worsen the
future scal burden, while higher mortality rates will alleviate the problems. In Section 4.7,
I explore the sensitivity of the results to increased life expectancy.
8
3.2 Eciency unit proles, preferences and technology
Estimates of the eciency unit proles for each type s are taken from Storesletten (1995).5
This implies that immigrants who came when they were, say, 27 years old, earn, on average,
2% less than natives over their remaining lifetime and those who immigrated when 37 years
old earn 13% less than natives. These estimates are in line with e.g. LaLonde and Topel
(1992) and somewhat below those of Chiswick (1978). Since the public nance implications
of immigration are sensitive to the labor income of natives, I also try an alternative earnings
prole where immigrants earn 10% less than my estimates. The skills of immigrants are
measured as completed education and divided into three groups: (1) \low-skilled" - high
school or less, (2) \medium-skilled" - more than high school but less than a bachelor's
degree, and (3) \high-skilled" - a bachelor's degree or more. This distributes the recent
immigrants in the 1990 Census into three roughly equally sized skill groups.
The functional form of the utility function (2) implies a unit elasticity of substitution between
consumption and leisure, which is motivated by fairly constant annual hours worked per
household in the postwar period. The parameter is set to 0.33, see Ros-Rull (1996), and
the inverse of the intertemporal elasticity of substitution, , is set at 4, since a period in the
model is fairly long. The time preference parameter is set to 1:011 (annualized), based on
estimates from Hurd (1989).
The technology is standard. I assume a standard Cobb-Douglas production function taking
labor and capital as inputs, Yt = zt Kt Nt1; . Following Cooley and Prescott (1995), the
capital's share of income, , and the (annualized) depreciation rate, , are set to 0.4 and
4.8%, respectively. The steady state growth rate in consumption per capita, ;, is 1.5%
(annualized), which equals the average annual US growth rate in GNP per capita over the
last two decades.
3.3 Government
The income tax rate of the \status quo" scal policy is calibrated to = 28:2%, which would
make total tax revenues amount to 32.5% of output in the rst period of the \scal reform"
economy, the same as total federal, state and local tax revenues in 1993.6 The payroll tax,
p, is set to 15.3% of labor income.
The age-specic government consumption levels, gi in (3), are taken from Auerbach, Kotliko, Hagemann and Nicoletti (1989), and scaled so that overall government consumption
is 16.1% of GNP in the rst period of the scal reform economy, the same as in 1993.
I assume all workers, except illegal immigrants, to be enrolled in Social Security. The Old
Age Insurance formula is a function h(:) of average indexed earnings, indexed at rate ;.7 The
9
age-specic lump sum transfers from the remaining components of Social Security, including
Medicare, are estimated from unpublished data from the Social Security Administration. All
agents who have contributed to the Social Security system for more than ten years qualify
for benets according to US law. Using historical immigration gures and the calibrated
return migration process, I nd that 930,000 return migrants did qualify for Social Security
benets in 1970. Warren and Peck (1980) report that only 230,000 return migrants actually
did collect benets in 1970 (many countries have bilateral treaties with the US limiting the
scope of collecting benets from more than one country). Hence, I assume that =25%
of the return migrants claim the benets to which they are entitled. Moreover, age-specic
lump sum transfers to return migrated agents, ^i, contain only Survivor's Insurance and
Disability Insurance.
All other transfers on federal, state and local level, which added up to 7% of GNP in 1993, are
distributed evenly on all natives and legal immigrants as part of i. Aggregate government
transfers in the rst period, T1 , are then 14.4% of GNP in the scal reform economy, the
same as the total federal, state and local transfers and subsidies in 1993.
3.4 Initial conditions
I use the 1992 distribution of natives as the initial condition for the population. The initial
distribution of immigrants across age and skills is taken from the 1990 Census. 3.2 out of the
initial 8 million low-skilled immigrants are assumed to be illegal residents (Fix and Passel
(1994)).
The initial government debt, which consists of nancial assets of the federal, state and local
governments, is set to 50% of GNP (in the scal reform economy). The initial distribution
of assets equals the steady state distribution of assets scaled so that the initial capital to
output ratio is 3.3. The steady state capital to output ratio in this economy is 2.4, and agents
must hold 126% more wealth than in steady state to reach 3.3.8 In Storesletten (1999), I
document that the results are quite robust to the choice of initial capital stock.
4 Findings
The model is solved by using a method related to the Auerbach and Kotliko (1987) approach, see Storesletten (1999) for details.9
10
4.1 Fiscal reform
Before turning to the immigration policy reform experiments, I will briey describe the scal
reform economy, where the current immigration policy is pursued and the budget is balanced
through a once-and-for-all tax increase in the rst period.
The equilibrium income tax rate in this economy is 32.6%, 4.4% points higher than the
\status quo" tax rate of 28.2%. Thus, a once and for all immediate tax hike of 4.4%
points would preempt the need for any future scal reform associated with the demographic
transition.
The aggregate capital stock falls sharply during the rst periods. This is due to a relatively
high initial wealth to output ratio (3.8 in the rst period, compared to 2.0 in steady state).
Consequently, the rate of return on capital (before tax) rises from 6.8% in the rst period to
10.0% in steady state, and the initial growth rates in GNP per capita are lower than ;. All
the immigration reform economies below, exhibit a similar pattern. Note that the steady
state age proles of consumption and work eort in the theoretical economies t reasonably
well with the data (Ros-Rull (1996) and Storesletten (1999)).
4.2 Immigration policy reform
This paper investigates if immigration policy reform alone can be used as an instrument for
satisfying the government's long-run budget constraint, given that current tax and spending
policies remain unchanged, i.e. when equals its \status quo" level of 28.2%. To this end,
I explore a particular type of selective policies: let future immigration of each age and skill
group of legal immigrants be some xed fraction of the population. For each single age-skill
group of new legal immigrants, I compute the smallest annual inow of such immigrants,
over and above the status quo ows of immigrants, that would balance the budget in the
long run.
The rst four rows in Table 1 summarize the key results for the benchmark calibration.
Within this class of policies, I nd that the budget can be balanced with a sucient inow of any age group of high-skilled immigrants between 20 and 54. If the attention is
restricted to immigrants below 20 or above 54, however, the budget cannot be balanced
without increasing taxes or reducing government spending. For medium-skilled immigrants,
the feasible age range is 25-49, while no positive inow of legal low-skilled immigrants can
balance the government budget.
40{44 year old high-skilled immigrants is the group with the lowest fraction of new immigrants required to balance the budget: 0.617% annually, or about 1.6 million, compared
to 0.44% today. This policy will be referred to as the \immigration reform" policy and if
11
pursued, the steady state population growth would be 0.9% annually.
Thus, to the extent that an immigration reform which involves the admission of 1.6 million 40{44 year old high-skilled immigrants annually is feasible, the government can choose
between this reform and an income tax hike of 4.4% points. While admitting 1-2 million
high-skilled immigrants might be feasible from a domestic political point of view, attracting
such a large number of high-skilled middle aged immigrants might, in practice, be a bigger
obstacle to feasibility. In comparison, the number of high-skilled 25{49 year old immigrants
required to balance the budget is 1.8 million, or 0.70% of the population annually (simple
average across age groups 25{49 in Table 1). Currently, only 15.0% of the new immigrants,
about 160,000 annually, are 25{49 years old and high-skilled (according to the 1990 Census
5% sample). But even though the prospects of achieving, say, an eleven-fold increase of this
gure might be slim, tripling or quadrupling the size of this group would still go a long way
in alleviating the need for scal reform.
The strong scal impact of immigration can be further demonstrated by considering the
evolution of the debt to output ratio in the immigration reform economy, which declines
from 50% of GNP in 1995 to -21% of GNP in year 2040. The government budget, excluding
interest payments, is running a surplus from 1995 to 2035, while the government runs a
decit until 2000 if interest payments are included, ve years more than in the scal reform
economy.
These calculations incorporate the general equilibrium eects of immigration, which can be
expected to suppress the net benets of immigrants. If immigration is not associated with a
capital inow (as I have assumed here), an increase in immigration increases the interest rates
and reduces the wages. Consequently, the cost of servicing the public debt increases, and the
tax revenues fall, as most tax revenues are collected from labor under the US tax system.
These eects are quantitatively large. Consider, for example, the impact of abstracting from
general equilibrium eects when re-calculating on the number of 40-44 year old immigrants
required to balance the budget. If the prices are held xed and equal to those of the scal
reform economy { where the status quo immigration policy is being pursued {, the required
number of immigrants decreases by one fth, to 0.48% of the population per year.
4.3 Net present value calculations
To understand these ndings, it is illuminating to consider the net discounted gain to government of admitting one extra immigrant. Since the aim is to compute the scal impact under
the status quo scal policy, the immigration reform economy is used as a starting point for
the net present value calculations. These are partial equilibrium exercises in that potential
changes in prices and bequests due to increased immigration are ignored.
12
Let J (i; s; t) denote tax revenues minus government consumption and transfers directly incurred by an agent (i; s) in period t. Simply computing the net present value of fJ (i; s; )gIi=s(1)
is not sucient for determining the net contribution of an immigrant, however. One must
also include the cost or gain associated with potential future children, grandchildren, etc.
The net discounted gain, NPV(s; t), including the cost of future children, of receiving one
new immigrant (or native newborn) of type s in period t, must then satisfy
NPV(s; t) =
I
X
i=s(1)
(J (i; s; t + i ; s(1)) +
!
NPV(0; t + i ; s(1) + 1) (1 + Rt )=ij;=0s(1)(1 + Rt+j );
+ 1 + Ri;s
t+i;s(1)+1
(6)
where NPV(0; t) denotes the NPV of a native newborn in period t. This gure is computed
by applying (6) recursively and found to be -$88,000. Note that a negative NPV of newborn natives can be consistent with long-run government budget balance, because there is a
sucient number of working-age agents alive, whose NPV of remaining tax revenues minus
expenditures are large and positive.
4.3.1 Impact of skills
NPV proles across age and skills for new immigrants are displayed in Figure 1. All NPV
gures are reported in 1993 dollars and use the prices and scal policy of the immigration
reform economy. The \skill" of an adolescent immigrant is dened as the education she will
acquire in the future. Thus, the NPV of, say, a \low-skilled" adolescent immigrant is the
NPV conditional on her being low-skilled her entire life.
The results reveal dramatic dierences in scal impact across these groups: net government
gain of new immigrants ranges from -$94,000 for an infant immigrant, conditional on being
low-skilled during her entire life, to $177,000, or 7.0 times annual GNP per capita, for a
40{44 year old high-skilled immigrant. Thus, denying a prospective 40{44 year old highskilled immigrant a visa is expected to cost the government $177,000. These results are
quantitatively similar to those of Lee and Miller (1997).
<Figure 1 about here>
Conditional on age, the NPV of high-skilled immigrants exceed the NPV of medium-skilled
immigrants which, in turn, dominate the NPV of low-skilled immigrants, except for immigrants past the retirement age. In fact, the NPV of low-skilled immigrants is negative for
all age groups, which explains why no positive inow of low-skilled immigrants would suce
to balance the budget. In contrast, all high-skilled working-age immigrants yield a positive
NPV.
13
All age proles exhibit a strong hump-shape which peaks between 35 and 44, reecting a
trade-o between a longer remaining working life on the one hand, and a smaller number
of new children on the other. The local maximum for 60{64 year old immigrants is due
to the minimum requirement of ten years of Social Security contributions for receiving full
benets. Thus, 55{59 year old immigrants is the oldest group which can enjoy full Social
Security benets during retirement. After 65, all groups coincide (since skills by assumption
distinguish immigrants on productivity only). The NPV of retired immigrants increases
monotonically with age as the remaining lifetime becomes shorter.
The global maximum occurs later for high-skilled immigrants (40{44) than for mediumand low-skilled immigrants (35{39). Social Security benets relative to tax contributions are
lower for the high-skilled than for the other skill groups, so getting to the peak earnings years
(40{60) more quickly becomes relatively more important than avoiding the costs associated
with retirement. If the cost of children is excluded (which is equivalent to a zero fertility
assumption), the peak NPV comes 5{10 years earlier for the low- and medium-skilled. Including the cost of children is of most importance for immigrants who arrive before 35. If the
cost of children was excluded, the NPV of this group would be $29,000 higher. The timing
of the peak is also inuenced by the discount rate. If the sequence of individual net contributions, fJ (i; s; )gIi=s(1), is discounted at, say, 4% (annualized) instead of the equilibrium
return on capital, the NPV proles would peak at 30{34 for all skill groups. With a lower
discount rate, the peaks shift to the left, since the costly retirement years are discounted to
a smaller extent.
Given the empirical age structure of new immigrants currently admitted to the US, I can
compute the government gain, in net present value terms, of admitting one additional \representative" legal immigrant, by weighting the age structure of current new immigrants with
the net present value proles in Figure 1. This yields a net discounted gain of a mere $7,400.
When conditioning on skills, I nd the NPVs of representative high-, medium-, and lowskilled immigrants, to be $96,000, -$2,000, and -$36,000, respectively. In contrast, the NPV
of a representative illegal immigrant is -$54,000, given the rather extreme assumptions that
they incur the same government consumption as natives, pay no taxes, receive no transfers,
and have the same return migration process as legal immigrants.
4.4 The role of return migration
Return migration is an important part of the demographic process, and, to the extent that
public policy can inuence return migration, one would like to understand its impact on
public coers. To this end, I contrast the benchmark return migration process to a polar case
of no return migration. The NPV proles for high-skilled immigrants, displayed in Figure 2,
reveal that reducing return migration to zero would increase the NPV of 5{49 year old
14
immigrants and reduce the NPV for others. The calibrated return migration process implies
substantial emigration after the rst (ve-year) period, so groups facing a long sequence
of positive (negative) contributions to government in the near future, will see their NPV
increase (decrease), if return migration is decreased.
<Figure 2 about here>
This picture is mirrored for the calculations regarding the ows of immigrants required to
balance the budget, see row 7 of Table 1. A smaller number of new immigrants are required
for all age groups between 20{49, while a slightly larger number are needed for the 50{54
year old high-skilled immigrants.
4.5 The role of family migration
Admitting adult immigrants but excluding their (already existing) children may not be
politically feasible. To understand the impact of family migration, I contrast the benchmark
single immigrants case with a case where immigrants bring children who are 15 years old
or younger and leave their older children behind. The children are assumed to be mediumskilled, and the distribution of an immigrant's children is computed, conditional on her age,
by assuming pre-migration fertility rates to be a xed fraction of native fertility, where this
fraction is set so that the inow of immigrants under 15 matches the data.
The dashed line in Figure 2 illustrate the eect of family unit migration on the NPV prole
of high-skilled immigrants. The numbers denote NPV per head of household, including
her children brought from the emigration country. The eects are considerable; the NPV
of 20{50 year old immigrants decreases by $37,000 relative to the single immigrant case.
The impact is largest for 30{39 year old immigrants, whose NPV is reduced by $56,000, on
average. This is due to the fact that these families have the largest number of children under
15, on average 1.53 per adult family member, according to my calculations.
This picture is largely conrmed when considering the number of immigrants (including
children) required for balancing the budget; the minimum annual number increases to 1.08%
of the population. The head of the household is then assumed to be high-skilled and 45{49
years old (see row 5 of Table 1), ve years older than those for whom the NPV prole peaks.
The discrepancy is due to the fact that, even though each 40{44 year old immigrant has a
higher NPV, including children, the size of their households are larger than those headed by
45{49 year old agents.
15
4.6 Static accounting exercises
Borjas (1994), Huddle (1993) and Passel (1994) quantify the gain on immigration in a static
accounting framework by computing the government surplus or cash ow in one particular
year of all immigrants currently residing in the US, and nd this gure to be -$16 billion,
-$40 billion, and $27 billion, respectively (1993 gures). To contrast my ndings to these
previous studies, I perform a similar exercise with my model. I consider the current scal
policy and the current immigration policy, disregarding that this combination is infeasible,
and using the prices of the immigration policy reform experiment. I then compute the net
government surplus in the rst period, resembling the 1993-1997 period, to be about 0.32% of
GNP, or $21 billion in 1993, which is within the range of the previous studies. Note that the
current age distribution of immigrants is favorable, since the surge in immigration is a recent
phenomenon. If a similar static accounting exercise is performed for future periods, it will
produce negative numbers after six periods (30 years), provided the status quo immigration
policy is continued.
4.7 Sensitivity analysis
To check the sensitivity of the absence of public goods assumption, I assume, alternatively,
that part of government consumption provides a nonrival public good and that future public
goods expenditures, in levels, is a xed fraction of government consumption in the scal
reform economy. Thus, additional immigrants do not increase the public goods provision,
and the immigrants' net contributions, J (i; s; t), are increased accordingly. I set the fraction
of public goods in government consumption to 31%, which equals the 1990{94 share of
national defense, foreign aairs, and general science, space and technology in government
purchases of goods and services. Moreover, agents' preferences are assumed to be additively
separable over the public good on the one hand, and the standard private consumption{
leisure composite on the other, so that the provision of public goods does not aect the
agents' decisions. In this case, the NPV of new immigrants increase by a substantial $19,000
on average; the younger the immigrants, the larger the increase ($21,000 for the 0-4 year
old).
The benchmark calibration implies a life expectancy of 77 years. The SSA population projections, for instance, assume life expectancy to increase gradually and reach 82 years by
2075. To explore how sensitive the results are to the mortality assumptions, I study an
extreme case where life expectancy is 82 years from period one. Under this demographic
scenario, the implied dependency ratios exceed the SSA projections until 2050 and reaches
a maximum of 0.399 in 2035. The income tax hike and inow of high skilled immigrants
aged 40{44 required to balance the budget are, in this case, 5.6% and 0.80%, respectively,
compared to 4.4% and 0.62% under the benchmark mortality assumptions.
16
All results are sensitive to the wage income of immigrants. To illustrate this, I explore the
case where immigrants earn 10% less than in the benchmark case, which reduces the net
benets of immigration signicantly. For example, the NPV of 40{44 year old high-skilled
immigrants falls by about one sixth, or $31,000, and the NPV of a representative immigrant
falls to -$6,000. The minimum number of new high-skilled immigrants required to balance
the budget increases to 0.80% of the population (see row 6 in Table 1).
5 Conclusion
This paper demonstrates that immigration can have strong quantitative implications for US
scal policy. In particular, the paper investigates if an immigration policy reform alone could
resolve the future scal problems associated with the ageing of the baby boom generation.
Using a calibrated general equilibrium overlapping generations model, which explicitly accounts for key dierences between immigrants and natives, Social Security and the demographic transition, I nd that immigration policies sustaining the current scal policy do
exist and are characterized by increased inow of middle aged high- and medium-skilled
immigrants. Admittedly, the American public seems opposed to such large increases in immigration. However, when faced with the trade-o between higher taxes on the one hand
and a larger number of high-skilled immigrants on the other, it seems reasonable that a
majority would, on the margin, opt for increasing the number of immigrants.
These ndings are illustrated by computing the net government gain, in present value terms,
of admitting one additional immigrant to the US, conditional on age and skills at the time
of immigration. This discounted gain varies considerably across the age and skills of new
immigrants, with large and positive gures for high- and medium-skilled working-age immigrants.
Thus, rather than viewing immigration as a problem, the perspective should be one of
considering high- and medium-skilled working-age migrants as an attractive resource, for
which various countries compete. Moreover, to the extent one is willing to use immigration
for generating revenues, the immigration policy should involve attempts to actively attract
such immigrants. This analysis has described how some of the migration rents go to natives
via the government. A larger share of these rents could be seized, however, by deviating
from the principle of taxing natives and legal immigrants at the same rates, although such
reforms would have to be traded o against the reduced attractiveness of the US as a host
country.
17
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20
1 For
instance, Gustman and Steinmeier (1998) show, using data from the Health and Retirement Survey, that immigrants have, on average, provided a postive net contribution to
social security.
2 Although the economic eects of immigration have received substantial attention, the main
focus of the literature has been on the impact on employment and wages for natives (see e.g.
Friedberg and Hunt (1995) for a survey).
3 This specication abstracts from possible dierences between immigrants and natives in
the utilization of government transfer programs. Borjas and Hilton (1996) document that
immigrants have a higher participation rate in welfare programs than natives. Fix, Passel and
Zimmermann (1996) argue that these dierences are explained by the higher welfare program
participation rate among refugees and retired immigrants (who, presumably, do not qualify
for Social Security benets). My focus, however, is on labor migrants; that is, workingage legal immigrants who will most likely qualify for Social Security when old. Moreover,
my measure of i encompasses all government transfers (net of OAI), including programs
where natives may well have a higher participation rate, like unemployment insurance or
survivors' insurance. In the case of Canada, where labor immigrants are explicitly targeted,
the welfare participation rate among immigrants is lower than among natives (Baker and
Benjamin (1995)).
4 This implies a nal total fertility rate of 2.23, compared with 2.25 in the middle projections
of the U.S. Bureau of the Census (1992).
5 The estimation technique involves accounting for changes in national origin, gender, and the
age of new immigrants over the 1950{90 period. This requires aggregation over sex, national
origin, etc. The approach in is to divide the 5% 1990 Census sample into 15 3 12 6 2
boxes (age, education, age at the time of immigration, region of origin, and sex), and to
compute the average wage for each box. The eciency unit proles for new immigrants are
then computed as weighted averages over these boxes, where the relative weights of each
box is based on the 1988-1990 cohorts of immigrants. \Cohort eects" should not be a
problem, as observables are controlled for (LaLonde and Topel (1992)). Since legal status is
not identied in the 1990 Census, I assume that no dierences in wages between legal and
illegal immigrants are left after controlling for education, region of origin, age, age at the
time of immigration, and sex.
6 For calibrating several model parameters, I use, as a benchmark, a \scal reform" economy where the current immigration policy is pursued and the budget is balanced through
increasing taxes. Note that the equilibrium tax rate in the scal reform economy exceeds
the status quo tax rate.
7 The formula is standard; h is piecewise linear with two \bend points," which are set to 20%
and 122% of GNP per capita. The replacement rates (i.e. slopes of h) within brackets 1, 2,
21
and 3 are 90%, 32%, and 15%, respectively.
8 Note that there is, at most, one stable steady state for a given pair of immigration policy
and scal policy. As attention has been restricted to policies that are constant over time,
the initial conditions and immigration policy will determine the lowest constant income tax
rate, , satisfying equilibrium condition (e). Equally, the equilibrium condition (e), the
initial conditions, , and a particular distribution of new immigrants, pin down the required
number of new immigrants and the future path of government debt. If the tax rates or the
immigration policy were allowed to vary over time, however, the need for higher taxes or
increased immigration during the demographic transition could be alleviated by aiming at a
higher long-run debt to output ratio, for example.
9 In a nutshell, the idea is to iterate on the tax rate or immigration policy and, for every iteration, solve for a nite equilibrium price sequence, given initial conditions and the assumption
that the economy is in steady state after 50 periods. The approximations are quite accurate,
as the economies converge well before they are supposed to be in steady state. For instance,
after 30 periods { or 150 years { the annualized rate of return on capital has typically been
less than 10 basispoints away from its steady state value in the economies I have considered.
22
Figure 1
200
150
← High−skilled
NPV in $ 1,000
100
Medium−skilled
↓
50
0
↑
Low−skilled
−50
←−−−−−−− Native newborn
−100
0
10
20
30
40
50
60
70
80
90
Age
Discounted net public gain of admitting additional immigrants, conditional on age and skills.
23
Figure 2
200
← Benchmark (high−skilled)
150
No return
migration →
NPV in $ 1,000
100
← Family unit
immigration
50
0
−50
← Native newborn
−100
0
10
20
30
40
50
60
70
80
90
Age
Discounted net public gain of admitting additional immigrants { return migration and family
units.
24
Experiment
Age of new immigrants:
20-24 25-29 30-34 35-39 40-44 45-49 50-54
Baseline (high skilled) 1:89 0:84 0:66 0:62 0:62 0:77 2:01
Medium skilled
3:13 2:01 1:79 2:13 3:86
Low skilled
Averaged over skills
2:23 1:50 1:40 1:67 3:61
Family unit
4:20 2:06 2:02 1:57 1:10 1:08 2:06
Low earnings
1:20 0:90 0:80 0:80 1:10 3:52
No return migration 1:17 0:65 0:54 0:50 0:53 0:74 2:43
Table 1: Annual immigration (in percent of population) required to balance the government
budget if the scal policy is kept unchanged. A dash - means that no positive number of
immigrants was large enough to balance the budget in the long run.
25